Two possibilities spring to mind:

When the switch is on, you should find two live feeds at the wiper motor. When it's off, only one should be live. If both remain live, then the switch (or the relay if there is one in the circuit) is at fault.

If not, then the most likely culprit is the parking switch in the wiper motor box itself. When you switch the thing off, the switched feed is cancelled but the permanent feed, via the parking switch, remains live. When the wiper reaches its parked position, the parking switch operates and it stops. Thus if the parking switch is sticking or failed, it'll keep going in perpetuity. In the past I have found that dried old grease can cause wiper motor parking switches to stick long enough to make it past park without activating. If the parking switch is the problem, dismantling the wiper motor to get at the park switch, cleaning everything up and regreasing often cures the problem.